2a*2x + 2a*y this is the same equation, only we've split 4ax into 2a*2x and 2ay into 2a*y

2a*(2x+y) you've factored 2a out of the equation. Recall distribution: b*(c+d) = b*c + b*d always. This works backwards just as well...b*c+b*d = b*(c+d) which is what's been done here with b=2a, c=2x, d=y

2a*2x + 2a*y this is the same equation, only we've split 4ax into 2a*2x and 2ay into 2a*y

2a*(2x+y) you've factored 2a out of the equation. Recall distribution: b*(c+d) = b*c + b*d always. This works backwards just as well...b*c+b*d = b*(c+d) which is what's been done here with b=2a, c=2x, d=y

So what's the sticky point?

Hi Office_Shredder. Please stick with the original equation as the "learner" that's "me" is trying to achieve the understanding of the idea of "Factorisation" from first principles, therefore if you expand with more ideas before I gain the basics, I will be lost

am I right in thinking that the 2a on the left hand side of the equation has been moved to the right hand side, and the y placed inside the bracket?
When I multiply them out the original equation can be found, which seems right, but my understanding is that "if a number on the left hand side of the equals is positive, then moving it to the right hand side should make it negative"?

So; 4ax = 2a * 2x and 2ay = - 2a * y or is there different rules for different types of maths?